Question

For what value of p are 2p+1,13,5p-3 three consecutive terms of an ap

Answer 1

Solution:

Given 2p+1, 13 , 5p-3 are in AP.

To find: value of P

If a,b,c are in AP then we know that
2b=( a+c)
Here a= 2p+1
b=13
c=5p-3

2 (13) =(2p+1+5p-3)

26=7p-2

26+2=7p

28=7p

p=28/7 =4

Therefore the value of
P is 4.

Answer 2

Solution :-

If these terms are in AP then,

a₂ - a₁ = a₃ - a₂ = .............

a₂ = 13

a₁ = 2p + 1

a₃ = 5p - 3

⇒ 13 - (2p + 1) = (5p - 3) - 13

⇒ 13 - 2p - 1 = 5p - 3 - 13

⇒ - 2p - 5p = - 3 - 13 - 13 + 1

⇒ - 7p = - 29 + 1

⇒ - 7p = -28

⇒ 7p = 28

⇒ p = 28/7

⇒ p = 4

So, for the value of p = 4, these three consecutive terms are in AP.

Answer.